## Involve: A Journal of Mathematics

• Involve
• Volume 12, Number 3 (2019), 491-502.

### On the preservation of properties by piecewise affine maps of locally compact groups

#### Abstract

As shown by Cohen (1960) and Ilie and Spronk (2005), for locally compact groups $G$ and $H$, there is a one-to-one correspondence between the completely bounded homomorphisms of their respective Fourier and Fourier–Stieltjes algebras $φ : A ( G ) → B ( H )$ and piecewise affine continuous maps $α : Y ⊆ H → G$. Using elementary arguments, we show that several (locally compact) group-theoretic properties, including amenability, are preserved by certain continuous piecewise affine maps. We discuss these results in relation to Fourier algebra homomorphisms.

#### Article information

Source
Involve, Volume 12, Number 3 (2019), 491-502.

Dates
Received: 27 February 2018
Accepted: 9 September 2018
First available in Project Euclid: 5 February 2019

Permanent link to this document
https://projecteuclid.org/euclid.involve/1549335635

Digital Object Identifier
doi:10.2140/involve.2019.12.491

Mathematical Reviews number (MathSciNet)
MR3905343

Zentralblatt MATH identifier
07033144

#### Citation

Camungol, Serina; Morison, Matthew; Nicol, Skylar; Stokke, Ross. On the preservation of properties by piecewise affine maps of locally compact groups. Involve 12 (2019), no. 3, 491--502. doi:10.2140/involve.2019.12.491. https://projecteuclid.org/euclid.involve/1549335635

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